# [Gretl-users] Heteroskedasticity / correction

Ana Amaro ISG anaamaro at isg.pt
Fri Jan 10 13:27:23 EST 2014

```Hi
The test of this white Regression model does not have a constant...
Right?

Sent from my iPhone
Apologize for the brevity/grammar/spelling

No dia 10/01/2014, às 18:12, "Riccardo (Jack) Lucchetti" <r.lucchetti at univpm.it> escreveu:

>> On Fri, 10 Jan 2014, Ana Amaro ISG wrote:
>>
>> Hi everyone
>> I need some help on this topic:
>> 1- simple model one regressor (x)
>> 2- error is heteroskedastic (and residual analysis shows that the error variance increases with x variable)
>> 3- rerun the analysis dividing both model members by the sqrt(x) - no constant
>>
>> Eviews runs the white test with a constant
>> Gretl runs the white test with no constant!
>> The decision is, of course, different.
>>
>> Which software is doing it the right way? Eviews, right?
>
> Uhm, this is not what I'm seeing here.
>
> <hansl>
> nulldata 100
> set seed 987
> x = normal()
> e = normal() * sqrt(1 + x^2)
> y = x + e
>
> ols y x
> modtest --white
> </hansl>
>
> Of course, generating data which _does_ contain heterskedasticity is totally irrelevant here: if I understand the point correctly, the issue here is on whether a constant should be present or not in the auxiliary regression for the White test. And the answer is: yes, the constant should be there. And that's what gretl does:
>
> <output>
> ? ols y x
>
> Model 1: OLS, using observations 1-100
> Dependent variable: y
>
>             coefficient   std. error   t-ratio   p-value
>  --------------------------------------------------------
>  x           0.955352      0.128086     7.459    3.40e-11 ***
>
> Mean dependent var   0.340859   S.D. dependent var   1.747793
> Sum squared resid    201.0589   S.E. of regression   1.425096
> R-squared            0.359770   Adjusted R-squared   0.359770
> F(1, 99)             55.63201   P-value(F)           3.40e-11
> Log-likelihood      −176.8152   Akaike criterion     355.6305
> Schwarz criterion    358.2357   Hannan-Quinn         356.6849
>
> ? modtest --white
>
> White's test for heteroskedasticity
> OLS, using observations 1-100
> Dependent variable: uhat^2
>
>             coefficient   std. error   t-ratio   p-value
>  --------------------------------------------------------
>  x           −0.103511     0.315278    −0.3283   0.7434
>  sq_x         0.798762     0.152451     5.239    9.24e-07 ***
>
>
> Test statistic: TR^2 = 24.309362,
> with p-value = P(Chi-square(1) > 24.309362) = 0.000001
> </output>
>
>
>
> -------------------------------------------------------
>  Riccardo (Jack) Lucchetti
>  Dipartimento di Scienze Economiche e Sociali (DiSES)
>
>  Università Politecnica delle Marche
>  (formerly known as Università di Ancona)
>
>  r.lucchetti at univpm.it
>  http://www2.econ.univpm.it/servizi/hpp/lucchetti
> -------------------------------------------------------
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```